JP2006313216A - Oscillator device and optical deflector using the same - Google Patents

Oscillator device and optical deflector using the same Download PDF

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JP2006313216A
JP2006313216A JP2005135621A JP2005135621A JP2006313216A JP 2006313216 A JP2006313216 A JP 2006313216A JP 2005135621 A JP2005135621 A JP 2005135621A JP 2005135621 A JP2005135621 A JP 2005135621A JP 2006313216 A JP2006313216 A JP 2006313216A
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magnetic field
permanent magnet
oscillator
optical deflector
neutral position
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Susumu Yasuda
進 安田
Yukio Furukawa
幸生 古川
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Canon Inc
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Canon Inc
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Abstract

<P>PROBLEM TO BE SOLVED: To dispense with an accurate tuning operation in compensating an angular velocity of a scanning angle or a rotational angle in an oscillator device such as a resonance optical deflector. <P>SOLUTION: The oscillator device constituting a resonance optical deflector or the like is equipped with: supporting means 102, 103 which rotatably support an oscillator 101 in a range with a neutral position as the center around a nearly prescribed rotary shaft; restoring torque generating means 102, 104, 105, 108 which generate a restoring torque T in a direction returning the oscillator 101 to the neutral position; and driving means 106, 107, 108 which drive the oscillator 101 in a manner rotating and oscillating it with the neutral position as the center around the rotary shaft. The device has a nonlinear characteristic in which dT/dθ is smaller when the restoring torque T is monotonically decreases relative to displacement angle of arc θ from the neutral position of the oscillator 101, and in addition when the absolute value of the displacement angle becomes larger. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

本発明は、揺動体を略回転軸周りに回転して振動(回転振動)させる揺動体装置、それを用いた光偏向器などに関し、特に、機械共振を用いた共振型光偏向器の技術分野に関連する技術、この共振型光偏向器を使用した走査型ディスプレイやレーザービームプリンタやデジタル複写機等の画像形成装置に関するものである。 The present invention relates to an oscillating body device that rotates an oscillating body about a rotation axis (vibration), an optical deflector using the oscillating body device, and more particularly to a technical field of a resonant optical deflector using mechanical resonance. And an image forming apparatus such as a scanning display, a laser beam printer, or a digital copying machine using the resonance type optical deflector.

従来、ミラーが共振駆動される共振型光偏向器が色々と提案されている。共振型光偏向器は、ポリゴンミラー等の回転多面鏡を使用した光走査光学系に比べて、以下の様な特徴がある。すなわち、大幅に小型化が可能であること、消費電力が少ないこと、面倒れが理論的に存在しないこと、特に半導体プロセスによって製造されるSi単結晶からなる共振型光偏向器は理論上金属疲労が無く耐久性にも優れていること等の特徴がある(特許文献1参照)。 Conventionally, various types of resonant optical deflectors in which mirrors are driven to resonate have been proposed. The resonance type optical deflector has the following characteristics as compared with an optical scanning optical system using a rotating polygon mirror such as a polygon mirror. That is, it is possible to greatly reduce the size, power consumption is low, there is no inconvenience in theory, and the resonant optical deflector made of Si single crystal manufactured by the semiconductor process is theoretically metal fatigue. There is a characteristic that it has no durability and excellent durability (see Patent Document 1).

一方、ミラーが回転軸周りに回転振動する共振型光偏向器は、原理的にミラーの走査角(回転角)が正弦波的に変化するため、角速度が一定でないという特性がある。この特性を補正するために、以下の手法が提案されている(特許文献2参照)。 On the other hand, a resonance type optical deflector in which the mirror rotates and rotates around the rotation axis has a characteristic that the angular velocity is not constant because the scanning angle (rotation angle) of the mirror changes in a sinusoidal manner in principle. In order to correct this characteristic, the following method has been proposed (see Patent Document 2).

特許文献2においては、基本周波数とその3倍の周波数の振動モードを有する共振型偏向器を用い、基本波と3倍波を重ね合わせることで、略三角波駆動(回転振動における往路、復路の広い領域においてそれぞれ角速度が略一定の駆動)を実現している。この方法は、2つの振動モードを光偏向器作製時に正確に調律し、駆動時にそれら振動モードを利用することで角速度補正を行なうものである。
特開昭57−8520号公報 米国特許4,859,846号公報
In Patent Document 2, a resonance type deflector having a vibration mode having a fundamental frequency and a frequency three times that of the fundamental frequency is used, and the fundamental wave and the third harmonic wave are overlapped, so that a substantially triangular wave drive (wide forward and backward paths in rotational vibration) is achieved. In each region, the angular velocity is substantially constant). In this method, two vibration modes are accurately tuned when an optical deflector is manufactured, and angular velocity correction is performed by using these vibration modes during driving.
JP 57-8520 A U.S. Pat. No. 4,859,846

しかしながら、特許文献2に開示の方法は正確な調律作業を必要とするものである。 However, the method disclosed in Patent Document 2 requires an accurate tuning operation.

上記課題に鑑み、本発明の共振型光偏向器などを構成する揺動体装置は、揺動体を略所定の回転軸周りに中立位置を中心とする範囲で回転可能に支持する支持手段と、揺動体を中立位置に戻す方向に復元トルクTを発生する復元トルク発生手段と、揺動体を回転軸周りに中立位置を中心に回転して振動する様に駆動する駆動手段を有し、該復元トルクTが、揺動体の中立位置からの変位角θに対して単調減少し、かつ変位角θの絶対値が大きくなるとdT/dθが小さくなる非線形特性を有することを特徴とする。この非線形特性は、言い換えれば、揺動体の中立位置からの角度(絶対値)が大きくなるにつれ揺動体を中立位置方向に戻そうとするトルクが大きくなり、かつ中立位置からの角度(絶対値)が大きくなるにつれ中立位置方向に戻そうとするトルクの大きくなる変化率が大きくなるという特性である。ただし、復元トルクTやその変化率は常に変化する必要はなくて、略変化しない領域があってもよく、全体的に見て上記の様な変化をしていればよい。その設計は、所望される三角波駆動への補正程度などに応じて行えばよい。 In view of the above problems, an oscillating body device constituting the resonant optical deflector of the present invention includes a supporting means for rotatably supporting the oscillating body around a predetermined rotation axis in a range centered on a neutral position. A restoring torque generating means for generating a restoring torque T in a direction to return the moving body to the neutral position; and a driving means for driving the oscillating body to rotate around the rotation axis about the neutral position to vibrate. T has a non-linear characteristic that decreases monotonously with respect to the displacement angle θ from the neutral position of the oscillating body, and dT / dθ decreases as the absolute value of the displacement angle θ increases. In other words, this non-linear characteristic means that as the angle from the neutral position (absolute value) of the oscillating body increases, the torque for returning the oscillating body toward the neutral position increases, and the angle from the neutral position (absolute value). This is a characteristic that the rate of change in which the torque to be returned to the neutral position increases as the value increases. However, the restoring torque T and its rate of change need not always change, and there may be a region that does not substantially change, and it is only necessary to change as described above as a whole. The design may be performed according to the degree of correction to the desired triangular wave drive.

また、上記課題に鑑み、本発明の画像形成装置は、光源と、光源を変調する光源変調手段と、光偏向器として構成された上記構成の揺動体装置と、光源変調手段と光偏向器を制御する制御手段を有することを特徴とする。 In view of the above problems, an image forming apparatus of the present invention includes a light source, a light source modulating unit that modulates the light source, an oscillator device configured as an optical deflector, a light source modulating unit, and an optical deflector. It has the control means to control, It is characterized by the above-mentioned.

本発明によれば、共振型光偏向器などの揺動体装置の走査角ないし回転角速度の補正を行なうのに、正確な調律作業が不要になる。 According to the present invention, an accurate tuning operation is not required to correct the scanning angle or the rotational angular velocity of an oscillator device such as a resonant optical deflector.

本発明の揺動体装置の原理を図面を用いて説明しつつ、本発明の実施形態を説明する。なお、トーションバーの周りでねじり回転振動する偏向ミラーを持つ共振型光偏向器の原理として説明するが、この原理は、揺動体を略回転軸周りに回転振動させる揺動体装置の駆動にも一般的に当てはまるものである。 The embodiment of the present invention will be described while explaining the principle of the oscillator device of the present invention with reference to the drawings. The principle of a resonance type optical deflector having a deflecting mirror that twists and vibrates around a torsion bar will be described. However, this principle is generally used for driving an oscillating body device that oscillates an oscillating body about a rotation axis. Is true.

図8は、本発明の共振型光偏向器などの揺動体装置の原理を示すためのその一実施形態の模式図である。901は偏向ミラー、902はトーションバーである。偏向ミラー901は、2本のトーションバー902で弾性的に支持されており、2本のトーションバー902の他端は固定されている。共振型光偏向器は、偏向ミラー901に外部から加振力(共振のときは加振力というが、共振以外の駆動では駆動力という)を加えることで、共振を起こさせ、偏向ミラー901の駆動を行なう。ここでは、図9に示すように、偏向ミラー901の中立位置(トーションバーにねじれが生じていない位置であって、この位置を中心とする範囲で偏向ミラー901は回転振動する)からの変位角(回転角)をθ、軸周りに作用する復元トルクをTで表し、図中で右回りを正とする(逆でもよい)。本発明の共振型光偏向器などの揺動体装置においては、偏向ミラー901に作用する復元トルクTが、図10(A)、(B)に示すような特性を有することが特徴である。すなわち、復元トルクTは変位角θに対して単調減少し(途中にTが略一定となる様な所謂不感帯があってもよい)、変位角θの絶対値が大きくなるとdT/dθが小さく(その程度は問わなく、場合に応じて設定すればよい)なる非線形特性を持っている。この特性をバネとして考えると、中立位置からの変位角θの絶対値が大きくなるとバネ定数が増加するような非線形バネに相当する。 FIG. 8 is a schematic view of one embodiment for illustrating the principle of an oscillator device such as a resonant optical deflector of the present invention. Reference numeral 901 denotes a deflection mirror, and 902 denotes a torsion bar. The deflection mirror 901 is elastically supported by two torsion bars 902, and the other ends of the two torsion bars 902 are fixed. The resonance type optical deflector causes resonance by applying an external excitation force to the deflection mirror 901 (excitation force at the time of resonance, but driving force at driving other than resonance). Drive. Here, as shown in FIG. 9, the displacement angle from the neutral position of the deflection mirror 901 (the position where the torsion bar is not twisted and the deflection mirror 901 rotates and vibrates in the range centered on this position). (Rotation angle) is represented by θ, and the restoring torque acting around the axis is represented by T, and the clockwise direction in the figure is positive (or vice versa). The oscillator device such as the resonance type optical deflector of the present invention is characterized in that the restoring torque T acting on the deflection mirror 901 has characteristics as shown in FIGS. 10 (A) and 10 (B). That is, the restoring torque T decreases monotonously with respect to the displacement angle θ (there may be a so-called dead zone in which T becomes substantially constant in the middle), and dT / dθ decreases as the absolute value of the displacement angle θ increases ( The degree of non-linear characteristics may be set according to circumstances. Considering this characteristic as a spring, it corresponds to a non-linear spring in which the spring constant increases as the absolute value of the displacement angle θ from the neutral position increases.

ここで、偏向ミラー901の慣性モーメントをIとし、減衰を無視すると、本共振型光偏向器などの揺動体装置の運動方程式は、
I・dθ/dt=T(θ) (式1)
となる。図11(A)、(B)は、それぞれ、式1の運動方程式を満たすθ(t)、dθ(t)/dtを時間tに対してプロットしたものである。図11より、変位角θの絶対値が小さな中立位置付近では、復元トルクTが相対的に小さいため角速度変動(dθ/dtの変化)が少なくなり、また、変位角θの絶対値が大きい領域では、復元トルクTが相対的に大きくなるため角速度変動(dθ/dtの変化)が大きくなる様子が見て取れる。従って、復元トルクTに上記した様な非線形特性を持たせることで、揺動体装置の回転角速度を所望するように補正できることが分かる。
Here, if the moment of inertia of the deflection mirror 901 is I and the attenuation is ignored, the equation of motion of the oscillator device such as the resonance type optical deflector is
I · d 2 θ / dt 2 = T (θ) (Formula 1)
It becomes. FIGS. 11A and 11B are plots of θ (t) and dθ (t) / dt that satisfy the equation of motion of Equation 1 against time t, respectively. From FIG. 11, in the vicinity of the neutral position where the absolute value of the displacement angle θ is small, the restoring torque T is relatively small, so that the angular velocity fluctuation (change in dθ / dt) is small, and the region where the absolute value of the displacement angle θ is large. Then, since the restoring torque T becomes relatively large, it can be seen that the angular velocity fluctuation (change in dθ / dt) increases. Therefore, it can be understood that the rotational angular velocity of the oscillator device can be corrected as desired by giving the restoring torque T non-linear characteristics as described above.

以上のように、本発明においては、上述した様に、変位角をθ、復元トルクをTとすると、復元トルクTは変位角θに対して単調減少し、変位角θの絶対値が大きくなるとdT/dθが小さくなる(その絶対値は大きくなる)非線形特性をもっている。この非線形特性を利用することで、中立付近で角速度変動の小さな(すなわち三角波駆動に近づいた)共振型光偏向器などの揺動体装置を実現している。 As described above, in the present invention, as described above, when the displacement angle is θ and the restoration torque is T, the restoration torque T decreases monotonously with respect to the displacement angle θ, and the absolute value of the displacement angle θ increases. dT / dθ has a nonlinear characteristic that decreases (its absolute value increases). By utilizing this non-linear characteristic, an oscillator device such as a resonant optical deflector having a small angular velocity fluctuation (ie, approaching a triangular wave drive) near neutral is realized.

特に、本発明の共振型光偏向器などの共振型揺動体装置は、復元トルクTの非線形特性により、振幅が大きくなると共振周波数が高くなる傾向がある。この特性を利用すれば、振幅を制御することで、駆動周波数を制御することが可能な共振型光偏向器などの共振型揺動体装置を実現できる。 In particular, the resonance type oscillator device such as the resonance type optical deflector of the present invention tends to increase the resonance frequency when the amplitude increases due to the non-linear characteristic of the restoring torque T. By utilizing this characteristic, a resonant oscillator device such as a resonant optical deflector capable of controlling the drive frequency by controlling the amplitude can be realized.

次に、上記の如き特性の復元トルクを発生する本発明の復元トルク発生手段の原理について一実施形態を用いて説明する。図12は本発明の共振型光偏向器などの揺動体装置の一実施形態を回転軸の方向から見たときの概略図である(カンチレバー式の揺動体装置などでも原理は同じである)。905は偏向ミラー、906はトーションバー、907は可動永久磁石、908は静磁界Hである。 Next, the principle of the restoring torque generating means of the present invention for generating the restoring torque having the above characteristics will be described with reference to an embodiment. FIG. 12 is a schematic view of an embodiment of an oscillating device such as a resonant optical deflector according to the present invention as viewed from the direction of the rotation axis (the same principle applies to a cantilever-type oscillating device). 905 is a deflection mirror, 906 is a torsion bar, 907 is a movable permanent magnet, and 908 is a static magnetic field H.

図12に示すように、偏向ミラー905と可動永久磁石907の中立位置(図中水平方向)からの変位角をθとする。簡単のため、908の静磁界Hが一様であるとすると(実際には、例えば、周辺で弱くなっていてもよい)、可動永久磁石907に働くトルクTは、
=HMsinθ (式2)
で表される(図13(A)参照)。ここで、Mは可動永久磁石907の磁気モーメントである(この種のトルクは、磁気モーメント以外でも発生可能である)。
As shown in FIG. 12, the displacement angle from the neutral position (horizontal direction in the figure) of the deflection mirror 905 and the movable permanent magnet 907 is θ. For simplicity, assuming that the static magnetic field H of 908 is uniform (actually, for example, it may be weak in the periphery), the torque T m acting on the movable permanent magnet 907 is:
T m = HMsin θ (Formula 2)
(See FIG. 13A). Here, M is a magnetic moment of the movable permanent magnet 907 (this kind of torque can be generated by other than the magnetic moment).

一方、トーションバー906の復元力Tは、
=−kθ (式3)
で表される(図13(B)参照)。ここで、kはトーションバー906のねじりのバネ定数である(この種のトルクは、ねじり力以外でも発生可能である)。
On the other hand, the restoring force T s of the torsion bar 906 is
T s = −kθ (Formula 3)
(See FIG. 13B). Here, k is a torsion spring constant of the torsion bar 906 (this kind of torque can be generated by other than torsional force).

偏向ミラー905に作用する復元トルクTは、TとTの和であるから、
T(θ)=T+T=−kθ+HMsinθ (式4)
となる(図13(C)参照)。これより、復元トルクTは、変位角θの関数であり、変位角θに対して単調減少し、変位角θの絶対値が大きくなるとdT/dθが小さくなる非線形特性を持っていることが分かる。つまり、この復元トルクTは、変位角が大きくなるとバネ定数が大きくなるようなトーションバー、弾性バネなどのバネと等価な性質を持つことが読み取れる。また、式4より分かるように、静磁界Hを変化させることで、復元トルクTの非線形特性を制御することが可能になる。もちろん、バネ定数kを変化させても特性曲線を制御することができる。これらの設計は、所望する回転振動の周期、周波数、振幅、三角波駆動への接近程度などに応じて行えばよい。
Since the restoring torque T acting on the deflection mirror 905 is the sum of T m and T s ,
T (θ) = T m + T s = −kθ + HMsin θ (Formula 4)
(See FIG. 13C). From this, it can be seen that the restoring torque T is a function of the displacement angle θ, and has a non-linear characteristic that decreases monotonously with respect to the displacement angle θ and decreases dT / dθ as the absolute value of the displacement angle θ increases. . That is, it can be read that this restoring torque T has a property equivalent to a spring such as a torsion bar or an elastic spring whose spring constant increases as the displacement angle increases. Further, as can be seen from Equation 4, by changing the static magnetic field H, the nonlinear characteristic of the restoring torque T can be controlled. Of course, the characteristic curve can be controlled by changing the spring constant k. These designs may be performed according to the desired rotational vibration period, frequency, amplitude, degree of approach to triangular wave driving, and the like.

既に触れた様に、図10の如き復元トルクを生成する方法は上記の例に限らず、種々の方法が可能である。例えば、カンチレバー式揺動体における弾性バネによるトルクと上記の如き磁気モーメントによるトルクの組み合わせや、回転振動範囲の端付近で揺動体に当たってこれに復元トルクを与える板バネの如き付勢手段によるトルクと揺動体を殆ど自由に回転振動可能に支持する支持手段(例えば、非常に弱いねじりのバネ定数を持つトーションバー)によるトルクの組み合わせなどが可能である。後者の組み合わせの場合、図13(A)の復元力(この場合は磁気モーメントを利用していない)は、中立位置付近の変位角の領域では殆どゼロで、回転振動範囲の端付近の変位角の所で急に立ち上がる形となる(θがプラス側ではマイナスの方向に立ち上がり、θがマイナス側ではプラスの方向に立ち上がって、図13(C)の形をプラス側とマイナス側でもっと急峻に変化させた様な形となる)。一方、図13(B)の支持手段による復元力は殆どゼロで、変位角の横軸にほぼ沿った形となる。 As already mentioned, the method for generating the restoring torque as shown in FIG. 10 is not limited to the above example, and various methods are possible. For example, the combination of the torque by the elastic spring and the torque by the magnetic moment as described above in the cantilever-type oscillating body, or the torque and oscillating by the urging means such as a leaf spring that hits the oscillating body near the end of the rotational vibration range and gives this a restoring torque. A combination of torques by a supporting means (for example, a torsion bar having a very weak torsion spring constant) that supports the moving body so as to be able to rotate and vibrate almost freely is possible. In the case of the latter combination, the restoring force in FIG. 13A (in this case, the magnetic moment is not used) is almost zero in the region of the displacement angle near the neutral position, and the displacement angle near the end of the rotational vibration range. (Θ rises in the minus direction when the plus is on the side, and rises in the plus direction when the θ is on the minus side, and the shape of FIG. 13C becomes more steep on the plus and minus sides. It will be like a changed shape). On the other hand, the restoring force by the supporting means in FIG. 13B is almost zero, and the shape is substantially along the horizontal axis of the displacement angle.

以上のようにして、本発明においては、可動永久磁石などに作用するトルクとトーションバーなどの復元トルクを用いることで、中立付近で角速度変動の小さな共振型光偏向器などの揺動体装置を実現することができる。揺動体を回転軸周りに回転振動する様に駆動する駆動手段ないし加振手段については、下記実施例で説明する手段や、揺動体に着けた駆動電極と支持基板側の駆動電極に交互に電圧を印加することで揺動体に静電引力を作用させてこれを回転軸の周りに回転振動させる手段などがある。 As described above, in the present invention, by using a torque acting on a movable permanent magnet and a restoring torque such as a torsion bar, an oscillator device such as a resonance type optical deflector having a small angular velocity fluctuation near neutral is realized. can do. For driving means or vibration means for driving the oscillating body so as to oscillate around the rotation axis, voltage is alternately applied to the means described in the following embodiments, the driving electrode attached to the oscillating body and the driving electrode on the support substrate side. There are means for applying an electrostatic attractive force to the rocking body by applying and rotating it around the rotation axis.

以下、具体的な実施例を図に沿って説明する。 Hereinafter, specific examples will be described with reference to the drawings.

[実施例1]
図1(A)は、実施例1の共振型光偏向器の上面図、図1(B)はA−A’における断面図を表している。図1において、101は揺動体である偏向ミラー、102は偏向ミラーを支えるトーションバー(ここでは偏向ミラー101の両側に2つ用いているが、片側に1つ用いるのみでもよい)、103は支持部(トーションバー102と共に、偏向ミラー101を回転可能に支持する支持手段を構成する)、104は磁性材料からなる磁極、105は固定永久磁石、106は駆動コイル、107は磁性材料からなるコイル用磁心、108は偏向ミラーに着けられた可動永久磁石、110は基台、111はスペーサである。101〜103の要素は単結晶シリコン基盤をエッチングすることで一体に形成されており、偏向ミラー101の表面には光反射膜がコーティングされている。また、基台110とスペーサ111も金属材料から一体に形成されている。可動永久磁石108と固定永久磁石105は、N極とS極が図1中で示した方向になるように磁化されている。すなわち、可動永久磁石108はトーションバー102の回転軸を規定するねじりの軸に略直交し且つ揺動体の面に略平行な方向に磁化されており、固定永久磁石105により発生する磁界は、可動永久磁石108の磁化方向と略平行で向きが逆である。
[Example 1]
FIG. 1A is a top view of the resonance type optical deflector according to the first embodiment, and FIG. 1B is a cross-sectional view taken along line AA ′. In FIG. 1, 101 is a deflecting mirror that is a rocking body, 102 is a torsion bar that supports the deflecting mirror (here, two are used on both sides of the deflecting mirror 101, but only one may be used on one side), and 103 is supported. (Together with the torsion bar 102, which constitutes support means for rotatably supporting the deflection mirror 101), 104 is a magnetic pole made of a magnetic material, 105 is a fixed permanent magnet, 106 is a drive coil, and 107 is a coil made of a magnetic material A magnetic core, 108 is a movable permanent magnet attached to a deflection mirror, 110 is a base, and 111 is a spacer. The elements 101 to 103 are integrally formed by etching a single crystal silicon substrate, and the surface of the deflection mirror 101 is coated with a light reflecting film. The base 110 and the spacer 111 are also integrally formed from a metal material. The movable permanent magnet 108 and the fixed permanent magnet 105 are magnetized so that the north and south poles are in the directions shown in FIG. That is, the movable permanent magnet 108 is magnetized in a direction substantially perpendicular to the torsion axis that defines the rotation axis of the torsion bar 102 and substantially parallel to the surface of the oscillator, and the magnetic field generated by the fixed permanent magnet 105 is movable. The direction is substantially parallel to and opposite to the magnetization direction of the permanent magnet 108.

まず、本実施例の復元力(トルク)発生手段(トーションバー102、磁性材料からなる磁極104、固定永久磁石105、可動永久磁石108からなる)について説明を行なう。図2は、磁極104と固定永久磁石105が空間に作る磁界の磁力線191を示している。図2より、可動永久磁石108の近傍では、図2中で左から右へ略水平な磁界が生じていることが分かる。ただし、この空間の磁界は一様でなく、周囲に行くほど弱くなる。この空間に作られる磁界により、可動永久磁石108には図13(A)と同様な特性のトルクが働く。また、トーションバー102の弾性復元トルクは、図13(B)に示したような特性を示すので、結局、偏向ミラー101には、図13(C)に示すような復元トルクが作用する。それゆえ、本実施例の共振型光偏向器は、図11に示したような、中立位置を中心とした領域で角速度の変動が少ない回転振動運動を行なうことが分かる。 First, the restoring force (torque) generating means (including the torsion bar 102, the magnetic pole 104 made of a magnetic material, the fixed permanent magnet 105, and the movable permanent magnet 108) according to the present embodiment will be described. FIG. 2 shows magnetic field lines 191 of the magnetic field created by the magnetic pole 104 and the fixed permanent magnet 105 in the space. 2 that a substantially horizontal magnetic field is generated in the vicinity of the movable permanent magnet 108 from left to right in FIG. However, the magnetic field in this space is not uniform and becomes weaker toward the periphery. Due to the magnetic field created in this space, torque having the same characteristics as in FIG. 13A acts on the movable permanent magnet 108. Further, since the elastic restoring torque of the torsion bar 102 exhibits the characteristics as shown in FIG. 13B, the restoring torque as shown in FIG. Therefore, it can be seen that the resonance type optical deflector of this embodiment performs a rotational vibration motion with a small variation in angular velocity in a region centered on the neutral position as shown in FIG.

次に、本実施例の加振ないし駆動手段(共振のときは加振手段というが、共振以外の駆動では駆動手段という)について説明する。図3(A)は、コイル用磁心107の先端がS極になるようにコイル106に電流を流した場合の概略図である。図に示すように、磁力線はコイル用磁心107の底部から出て、その先端部に入るような形になり、可動永久磁石108には図中左回りにトルクが作用する(本実施例では、可動永久磁石108は復元トルク発生手段の構成要素であると共に駆動手段の構成要素でもある)。他方、図3(B)に示すように、コイル用磁心107の先端がN極になる向きにコイル106に電流を流すと、可動永久磁石108には図中右回りにトルクが作用することになる。つまり、コイル106に交番電流を流すことで、可動永久磁石108に対して磁化方向に略垂直に交番磁界を印加できて、可動永久磁石108を着けた偏向ミラー101を駆動できることが分かる。この際の駆動周波数を、偏向ミラー101の共振周波数と略等しくすることで、本実施例の共振型光偏向器を共振駆動することができる。 Next, a description will be given of the vibration or drive means (referred to as vibration means at the time of resonance, but referred to as drive means at driving other than resonance) according to the present embodiment. FIG. 3A is a schematic view when a current is passed through the coil 106 so that the tip of the coil magnetic core 107 has an S pole. As shown in the figure, the magnetic field lines come out from the bottom of the coil magnetic core 107 and enter the tip thereof, and torque acts on the movable permanent magnet 108 counterclockwise in the figure (in this embodiment, The movable permanent magnet 108 is a component of the restoring torque generating means and a component of the driving means). On the other hand, as shown in FIG. 3B, when a current is passed through the coil 106 in such a direction that the tip of the coil magnetic core 107 is N-pole, a torque acts on the movable permanent magnet 108 clockwise in the figure. Become. That is, it can be seen that by passing an alternating current through the coil 106, an alternating magnetic field can be applied to the movable permanent magnet 108 substantially perpendicular to the magnetization direction, and the deflection mirror 101 with the movable permanent magnet 108 can be driven. By making the drive frequency at this time substantially equal to the resonance frequency of the deflection mirror 101, the resonance type optical deflector of this embodiment can be driven to resonance.

以上説明したように、本実施例によれば、中立付近の角速度変動が小さい共振型光偏向器を実現できる。また、共振振動の振幅を制御することで(これは、例えば、コイル106に流す電流の強度の制御で行なう)、駆動周波数を制御することが可能な共振型光偏向器を実現できる。本実施例の共振型光偏向器においては、複数の共振周波数を合わせる必要が無いので正確な調律作業が不要である。また、複数の振動モードを同時に励振する必要が無いので、消費電力が少なくなる。また、構造が単純なため小型化が容易で、コストが安くなる。 As described above, according to the present embodiment, it is possible to realize a resonance type optical deflector having a small angular velocity fluctuation near neutrality. Further, by controlling the amplitude of the resonance vibration (this is performed, for example, by controlling the intensity of the current flowing through the coil 106), a resonance type optical deflector capable of controlling the drive frequency can be realized. In the resonance type optical deflector of this embodiment, it is not necessary to match a plurality of resonance frequencies, so that an accurate tuning operation is unnecessary. In addition, since it is not necessary to excite a plurality of vibration modes at the same time, power consumption is reduced. In addition, since the structure is simple, downsizing is easy and the cost is reduced.

[実施例2]
図4(A)、(B)は、それぞれ実施例2の共振型光偏向器の上面図と正面図を表している。図4において、201は偏向ミラー、202は偏向ミラーを支えるトーションバー、203は支持部、204は磁性材料からなる磁極、206A、206Bは静磁界発生コイル、210は基台である。220は加振アクチュエータであり、変形部材221と積層型圧電素子222A、222Bから構成されている。201〜203の要素は単結晶シリコン基盤をエッチングすることで一体に形成されており、偏向ミラー201の表面には光反射膜がコーティングされている。実施例1と同様に、偏向ミラー201の裏側には、可動永久磁石が配置されている(図4では不図示)。
[Example 2]
4A and 4B respectively show a top view and a front view of the resonance type optical deflector according to the second embodiment. In FIG. 4, 201 is a deflection mirror, 202 is a torsion bar that supports the deflection mirror, 203 is a support, 204 is a magnetic pole made of a magnetic material, 206A and 206B are static magnetic field generating coils, and 210 is a base. Reference numeral 220 denotes a vibration actuator, which includes a deformable member 221 and stacked piezoelectric elements 222A and 222B. The elements 201 to 203 are integrally formed by etching a single crystal silicon substrate, and the surface of the deflection mirror 201 is coated with a light reflecting film. Similar to the first embodiment, a movable permanent magnet is disposed on the back side of the deflection mirror 201 (not shown in FIG. 4).

まず、本実施例の復元力発生手段(トーションバー202、磁性材料からなる磁極204、静磁界発生コイル206A、206B、可動永久磁石(不図示)からなる)について説明を行なう。静磁界発生コイル206A、206Bに、磁極204の右側がS極、左側がN極になるように電流を流すと、可動永久磁石(不図示)の着いた偏向ミラー201には、実施例1と同様な復元トルクが作用する。それゆえ、本実施例の共振型光偏向器は、実施例1と同様に中立位置を中心とした領域で角速度の変動が少ない回転振動運動を行なうことが分かる。 First, the restoring force generating means (including the torsion bar 202, the magnetic pole 204 made of a magnetic material, the static magnetic field generating coils 206A and 206B, and a movable permanent magnet (not shown)) according to the present embodiment will be described. When a current is passed through the static magnetic field generating coils 206A and 206B so that the right side of the magnetic pole 204 is the south pole and the left side is the north pole, the deflection mirror 201 to which the movable permanent magnet (not shown) is attached is the same as in the first embodiment. A similar restoring torque acts. Therefore, it can be seen that the resonance type optical deflector of the present embodiment performs the rotational vibration motion with little fluctuation in the angular velocity in the region centered on the neutral position as in the first embodiment.

次に、本実施例の加振手段について説明を行なう。図5は、本実施例の加振アクチュエータ220の動作を説明する図である。積層型圧電素子222Aが縮み、222Bが伸びる向きに電圧を印加すると、変形部材221は図5で示したように変形し、支持部203を回転させる。積層型圧電素子222A、222Bの伸縮を逆にすれば、支持部203のトーションバー202の周りの回転方向は逆になる。これらのことから、2つの積層型圧電素子222A、222Bに交番電圧を印加することで、偏向ミラー201を駆動できることが分かる。この際の駆動周波数を、偏向ミラー201の共振周波数と略等しくすることで、本実施例の共振型光偏向器を共振駆動することができる。 Next, the vibration means of the present embodiment will be described. FIG. 5 is a diagram for explaining the operation of the vibration actuator 220 of this embodiment. When a voltage is applied in the direction in which the stacked piezoelectric element 222A contracts and 222B extends, the deformable member 221 deforms as shown in FIG. If the expansion and contraction of the stacked piezoelectric elements 222A and 222B is reversed, the rotation direction of the support portion 203 around the torsion bar 202 is reversed. From these facts, it is understood that the deflection mirror 201 can be driven by applying an alternating voltage to the two stacked piezoelectric elements 222A and 222B. By making the drive frequency at this time substantially equal to the resonance frequency of the deflection mirror 201, the resonance type optical deflector of the present embodiment can be driven to resonance.

本実施例の共振型光偏向器においては、静磁界発生コイル206A、206Bに電流を流すことで、中立付近の角速度変動が小さい共振駆動を行なうことができる。また、静磁界発生コイル206A、206Bに電流を流さなければ、通常の共振型光偏向器として用いることもでき、流す電流量で角速度変動の度合いと共振周波数を制御することができる。また、振幅を制御することで(これは、例えば、積層型圧電素子222A、222Bへの印加電圧の強度を制御することで行なう)、駆動周波数を制御することも可能である。また、本実施例の共振型光偏向器においても、複数の共振周波数を合わせる必要が無いので正確な調律作業が不要である。その他の点は実施例1と同じである。 In the resonance type optical deflector of the present embodiment, resonance driving with small angular velocity fluctuations near neutrality can be performed by passing a current through the static magnetic field generating coils 206A and 206B. Further, if no current is passed through the static magnetic field generating coils 206A and 206B, it can be used as a normal resonance type optical deflector, and the degree of angular velocity fluctuation and the resonance frequency can be controlled by the amount of current passed. The drive frequency can also be controlled by controlling the amplitude (for example, by controlling the intensity of the voltage applied to the multilayer piezoelectric elements 222A and 222B). In the resonance type optical deflector of this embodiment, it is not necessary to match a plurality of resonance frequencies, so that an accurate tuning operation is unnecessary. The other points are the same as in the first embodiment.

[実施例3]
実施例1及び実施例2では、揺動体をトーションバーのねじりの軸の周りで回転振動させていたが、揺動体を弾性体からなるカンチレバー式揺動体として、この振動体を固定端付近の根元部の撓みで回転振動させることもできる。図6は、こうした構成の実施例3の共振型光偏向器を示す断面図である。本実施例を示す図6において、501はカンチレバー式振動体である偏向ミラー、506は駆動コイル、508は偏向ミラーに着けられた可動永久磁石、510は基台、511は偏向ミラーの一端部を固定・支持するスペーサである。この構成では、復元トルク発生手段が、偏向ミラー501と一体に動くように取り付けられた可動永久磁石508と、可動永久磁石508に対して静磁界191を発生する静磁界発生手段と、支持手段の一部を構成する偏向ミラー501の固定端付近の撓み可能な根元部501aからなる。また、可動永久磁石508は、回転軸を規定するこの根元部501aの伸長方向(図6紙面に垂直な方向)に略直交し且つ偏向ミラー501の面に略平行な方向に磁化されており、静磁界発生手段の発生する磁界191は、可動永久磁石508の磁化方向と略平行で向きが逆である。
[Example 3]
In the first and second embodiments, the oscillating body is rotationally oscillated around the torsion axis of the torsion bar. However, the oscillating body is a cantilever-type oscillating body made of an elastic body, and this oscillating body is a base near the fixed end. It can also be rotated and vibrated by the bending of the part. FIG. 6 is a cross-sectional view showing the resonance type optical deflector according to the third embodiment having such a configuration. In FIG. 6 showing the present embodiment, reference numeral 501 denotes a deflecting mirror which is a cantilever vibrator, 506 denotes a drive coil, 508 denotes a movable permanent magnet attached to the deflecting mirror, 510 denotes a base, and 511 denotes one end of the deflecting mirror. It is a spacer that is fixed and supported. In this configuration, the restoring torque generating means includes a movable permanent magnet 508 attached so as to move integrally with the deflection mirror 501, a static magnetic field generating means for generating a static magnetic field 191 for the movable permanent magnet 508, and a supporting means. It consists of a deflectable root portion 501a in the vicinity of the fixed end of the deflection mirror 501 constituting a part. The movable permanent magnet 508 is magnetized in a direction substantially perpendicular to the extending direction of the base portion 501a that defines the rotation axis (direction perpendicular to the paper surface of FIG. 6) and substantially parallel to the surface of the deflection mirror 501. The magnetic field 191 generated by the static magnetic field generating means is substantially parallel to the magnetization direction of the movable permanent magnet 508 and opposite in direction.

本実施例のカンチレバー式偏向ミラー501の図6の矢印で示す回転振動も、加振ないし駆動手段である駆動コイル506と可動永久磁石508により、実施例1と同様に行われる。磁力線191の作用により中立位置を中心とした領域で角速度の変動が少ない回転振動運動が達成されることも、実施例1でほぼ述べた通りである。駆動コイル506の代わりに、実施例2で説明した積層型圧電素子を、偏向ミラー501の一端部を固定・支持するスペーサ511の所に用いて、実施例2の駆動方式にすることもできる。 The rotation vibration indicated by the arrow in FIG. 6 of the cantilever type deflection mirror 501 of the present embodiment is also performed in the same manner as in the first embodiment by the drive coil 506 and the movable permanent magnet 508 which are vibration or driving means. As described in the first embodiment, the rotational vibration motion with little fluctuation of the angular velocity is achieved in the region centered on the neutral position by the action of the magnetic lines of force 191. Instead of the drive coil 506, the stacked piezoelectric element described in the second embodiment can be used at the spacer 511 that fixes and supports one end of the deflection mirror 501, and the drive system of the second embodiment can be used.

この様な固定端付近の根元部501aの撓みを利用したカンチレバー式振動体を用いる実施例3でも、上記実施例と同様な効果を奏することができる。 The same effect as that of the above-described embodiment can be obtained in the third embodiment that uses the cantilever-type vibrating body that utilizes the bending of the root portion 501a near the fixed end.

[実施例4]
図7は、本発明の共振型光偏向器を用いた実施例4の光走査型ディスプレイを説明するための概略図である。レーザー光源303から射出されたレーザー光310は、本発明の第1光偏向器301で水平方向に走査され、次に第2光偏向器302で垂直方向に走査されて、スクリーン320上に画像を形成する。光偏向器301、302の駆動とレーザー光源303の変調発振は、制御装置304により同期して制御される。すなわち、制御装置304は、光源303を画像信号に基づいて変調する光源変調手段と、この光源変調手段と光偏向器301、302を制御する制御手段を含んでいる。
[Example 4]
FIG. 7 is a schematic diagram for explaining an optical scanning display of Example 4 using the resonant optical deflector of the present invention. The laser beam 310 emitted from the laser light source 303 is scanned in the horizontal direction by the first optical deflector 301 of the present invention, and then scanned in the vertical direction by the second optical deflector 302 to form an image on the screen 320. Form. The driving of the optical deflectors 301 and 302 and the modulation oscillation of the laser light source 303 are controlled in synchronization by the control device 304. That is, the control device 304 includes light source modulation means for modulating the light source 303 based on the image signal, and control means for controlling the light source modulation means and the optical deflectors 301 and 302.

水平方向走査手段として略三角波駆動が可能な本発明の第1光偏向器301を用いる本実施例の光走査型ディスプレイでは、fθレンズなどを用いることで水平方向に関して走査中央部と周辺部で走査速度の違いを少なくでき、良好な画像形成を実現することができる。また、本発明による光偏向器を用いているので、より小型で消費電力が小さく低コストの画像形成装置を提供できる。なお、本発明の揺動体装置は、その略三角波駆動を必要とするどの様な装置においても用いることができる。 In the optical scanning display of this embodiment using the first optical deflector 301 of the present invention capable of substantially triangular wave driving as the horizontal scanning means, scanning is performed at the scanning central portion and the peripheral portion with respect to the horizontal direction by using an fθ lens or the like. The difference in speed can be reduced and good image formation can be realized. Further, since the optical deflector according to the present invention is used, it is possible to provide an image forming apparatus that is smaller, consumes less power, and is low in cost. Note that the oscillator device of the present invention can be used in any device that requires its substantially triangular wave drive.

(A)は実施例1の共振型光偏向器の上面図であり、(B)は実施例1の共振型光偏向器の断面図である。(A) is a top view of the resonant optical deflector of the first embodiment, and (B) is a cross-sectional view of the resonant optical deflector of the first embodiment. 実施例1の共振型光偏向器の静磁界発生手段を説明する図である。It is a figure explaining the static magnetic field generation | occurrence | production means of the resonance type optical deflector of Example 1. FIG. 実施例1の共振型光偏向器の加振ないし駆動手段を説明する断面図である。FIG. 3 is a cross-sectional view for explaining excitation or driving means of the resonance type optical deflector according to the first embodiment. (A)は実施例2の共振型光偏向器の上面図であり、(B)は実施例2の共振型光偏向器の正面図である。(A) is a top view of the resonant optical deflector of the second embodiment, and (B) is a front view of the resonant optical deflector of the second embodiment. 実施例2の共振型光偏向器の加振ないし駆動手段を説明する図である。It is a figure explaining the excitation thru | or drive means of the resonance type optical deflector of Example 2. FIG. 実施例3の共振型光偏向器の断面図である。6 is a cross-sectional view of a resonance type optical deflector according to Embodiment 3. FIG. 実施例4の光走査型ディスプレイを説明する図である。It is a figure explaining the optical scanning type display of Example 4. FIG. 本発明の一実施形態の構成を説明する図である。It is a figure explaining the structure of one Embodiment of this invention. 本発明の原理説明に用いる記号を説明する図である。It is a figure explaining the symbol used for the principle explanation of the present invention. 本発明の復元トルクTを説明するグラフである。It is a graph explaining the restoring torque T of the present invention. 本発明の変位角θを説明するグラフである。It is a graph explaining displacement angle (theta) of this invention. 本発明(一実施形態で代表する)の復元トルクの発生原理を説明する図である。It is a figure explaining the generation | occurrence | production principle of the restoring torque of this invention (represented by one Embodiment). 本発明の復元トルクの発生原理を説明するグラフである。It is a graph explaining the generation | occurrence | production principle of the restoring torque of this invention.

符号の説明Explanation of symbols

101、201、501、901、905 揺動体(偏向ミラー)
102、202、902、906 トーションバー(支持手段、復元トルク発生手段)
103、203 支持部(支持手段)
104、204 磁極(復元トルク発生手段)
105 固定永久磁石(復元トルク発生手段)
106、506 駆動コイル(駆動手段)
107 コイル用磁心(駆動手段)
108、208、508、907 可動永久磁石(駆動手段、復元トルク発生手段)
191、908 静磁界H(復元トルク発生手段)
206A、206B 静磁界発生コイル(復元トルク発生手段)
220 加振アクチュエータ(駆動手段)
221 変形部材(駆動手段)
222A、222B 積層型圧電素子(駆動手段)
301 第1光偏向器(本発明の揺動体装置)
303 光源(レーザー光源)
304 制御装置(制御手段、光源変調手段)
506a 揺動体の根元部(支持手段、復元トルク発生手段)
101, 201, 501, 901, 905 Oscillator (deflection mirror)
102, 202, 902, 906 Torsion bar (support means, restoring torque generating means)
103, 203 Support part (support means)
104, 204 Magnetic pole (restoration torque generating means)
105 Fixed permanent magnet (restoration torque generating means)
106, 506 Driving coil (driving means)
107 Coil core (drive means)
108, 208, 508, 907 Movable permanent magnet (driving means, restoring torque generating means)
191, 908 Static magnetic field H (restoring torque generating means)
206A, 206B Static magnetic field generating coil (restoring torque generating means)
220 Excitation actuator (drive means)
221 Deformation member (drive means)
222A, 222B Multilayer piezoelectric element (drive means)
301 First optical deflector (oscillator device of the present invention)
303 Light source (laser light source)
304 control device (control means, light source modulation means)
506a oscillating body root (supporting means, restoring torque generating means)

Claims (10)

揺動体を略所定の回転軸周りに中立位置を中心とする範囲で回転可能に支持する支持手段と、揺動体を中立位置に戻す方向に復元トルクTを発生する復元トルク発生手段と、揺動体を回転軸周りに中立位置を中心に回転して振動する様に駆動する駆動手段を有し、該復元トルクTが、揺動体の中立位置からの変位角θに対して単調減少し、かつ変位角θの絶対値が大きくなるとdT/dθが小さくなる非線形特性を有することを特徴とする揺動体装置。 Support means for rotatably supporting the rocking body around a predetermined rotation axis in a range centered on the neutral position, restoring torque generating means for generating restoring torque T in a direction to return the rocking body to the neutral position, and rocking body Driving means for rotating the shaft around the neutral position to vibrate, and the restoring torque T monotonously decreases with respect to the displacement angle θ from the neutral position of the oscillator and is displaced. An oscillator device having non-linear characteristics in which dT / dθ decreases as the absolute value of the angle θ increases. 前記復元トルク発生手段が、前記揺動体と一体に動くように取り付けられた可動永久磁石と、可動永久磁石に対して静磁界を発生する静磁界発生手段と、前記揺動体に取り付けられた前記支持手段を構成するトーションバーからなり、可動永久磁石は、トーションバーの前記回転軸を規定するねじりの軸に略直交し且つ揺動体の面に略平行な方向に磁化されており、静磁界発生手段の発生する磁界は、可動永久磁石の磁化方向と略平行で向きが逆であることを特徴とする請求項1に記載の揺動体装置。 The restoring torque generating means is a movable permanent magnet attached so as to move integrally with the oscillating body, a static magnetic field generating means for generating a static magnetic field with respect to the movable permanent magnet, and the support attached to the oscillating body. The movable permanent magnet is magnetized in a direction substantially perpendicular to the torsion axis defining the rotation axis of the torsion bar and substantially parallel to the surface of the oscillating body. The oscillator device according to claim 1, wherein the magnetic field generated by is substantially parallel to and opposite to the magnetization direction of the movable permanent magnet. 前記揺動体がカンチレバー式に回転して振動する弾性体の揺動体であり、前記復元トルク発生手段が、前記揺動体と一体に動くように取り付けられた可動永久磁石と、可動永久磁石に対して静磁界を発生する静磁界発生手段と、前記支持手段を構成する揺動体の固定端付近の撓み可能な根元部からなり、可動永久磁石は、前記回転軸を規定する根元部の伸長方向に略直交し且つ揺動体の面に略平行な方向に磁化されており、静磁界発生手段の発生する磁界は、可動永久磁石の磁化方向と略平行で向きが逆であることを特徴とする請求項1に記載の揺動体装置。 The oscillating body is an elastic oscillating body that vibrates by rotating in a cantilever manner, and the restoring torque generating means is attached to a movable permanent magnet that is attached so as to move integrally with the oscillating body. It comprises a static magnetic field generating means for generating a static magnetic field and a bendable root near the fixed end of the oscillating body constituting the support means, and the movable permanent magnet is substantially in the extending direction of the root defining the rotating shaft. The magnetic field generated by the static magnetic field generating means is substantially parallel to and opposite to the magnetization direction of the movable permanent magnet, and is magnetized in a direction that is orthogonal and substantially parallel to the surface of the oscillator. 2. The oscillator device according to 1. 前記静磁界発生手段が、永久磁石を有することを特徴とする請求項2または3に記載の揺動体装置。 The oscillator device according to claim 2 or 3, wherein the static magnetic field generating means includes a permanent magnet. 前記静磁界発生手段が、コイルを有することを特徴とする請求項2または3に記載の揺動体装置。 The oscillator device according to claim 2 or 3, wherein the static magnetic field generating means includes a coil. 前記駆動手段が、前記可動永久磁石に対して磁化方向に略垂直に交番磁界を印加する交番磁界発生手段を有することを特徴とする請求項2乃至5のいずれかに記載の揺動体装置。 6. The oscillator device according to claim 2, wherein the driving unit includes an alternating magnetic field generating unit that applies an alternating magnetic field to the movable permanent magnet substantially perpendicular to the magnetization direction. 前記駆動手段が圧電素子を有することを特徴とする請求項2乃至5のいずれかに記載の揺動体装置。 6. The oscillator device according to claim 2, wherein the driving means includes a piezoelectric element. 前記駆動手段が、前記揺動体を前記回転軸周りに加振する加振手段であり、共振型揺動体装置を構成可能であることを特徴とする請求項1乃至7のいずれかに記載の揺動体装置。 The rocking device according to any one of claims 1 to 7, wherein the driving unit is a vibrating unit that vibrates the rocking body around the rotation axis, and can constitute a resonance-type rocking body device. Moving body device. 前記揺動体が偏向ミラーであり、光偏向器を構成することを特徴とする請求項1乃至8のいずれかに記載の揺動体装置。 9. The oscillator device according to claim 1, wherein the oscillator is a deflection mirror and constitutes an optical deflector. 光源と、光源を変調する光源変調手段と、請求項9に記載の光偏向器と、光源変調手段と光偏向器を制御する制御手段を有することを特徴とする画像形成装置。 An image forming apparatus comprising: a light source; a light source modulating unit that modulates the light source; an optical deflector according to claim 9; and a control unit that controls the light source modulating unit and the optical deflector.
JP2005135621A 2005-05-09 2005-05-09 Oscillator device and optical deflector using the same Pending JP2006313216A (en)

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